Finite Group Databasebeta

← Group #72220318

Character table — Group #72220318

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222244444444444444888888888888888888888888888888889999181818181818363636363636363636363636363654545454545454548181108108108108108108108108162
order12233663336666666666633333333666666666666666666666666444444121212121212121212121212121212121212888888882224242424242424242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11
χ31111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i-1
χ41111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii-1
χ511111111111111111111111111111111111111111111111111111-1-111-11111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1
χ611111111111111111111111111111111111111111111111111111-1-111-11111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1
χ711111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii11ii−i−i−i−iii1
χ811111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−iiiii−i−i1
χ911-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-11-11-11-11-1111-11-11-11-1-1
χ1011-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1-11-11-11-1111-11-11-11-11-1
χ1111-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1111111-1-1-1-1-1-111i−ii−i−ii−ii-1-1i−ii−i−ii−ii1
χ1211-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1111111-1-1-1-1-1-111−ii−iii−ii−i-1-1−ii−iii−ii−i1
χ1311-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-1111111-1-11-1-111-1-11-1-11-1-111-1-111
χ1411-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-111-1-111-11
χ1511-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111i−i−ii−iii−i11i−i−ii−iii−i-1
χ1611-11111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111−iii−ii−i−ii11−iii−ii−i−ii-1
χ172222-12-122-12-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220222-1-12-100000000-1-1-1-1002200220000-1-100-1-10
χ182222-12-122-12-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220222-1-12-100000000-1-1-1-100-2-200-2-200001100110
χ192222-12-122-12-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20-2-2-211-21000000001111002i2i00−2i−2i0000−i−i00ii0
χ202222-12-122-12-12222-1-122-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20-2-2-211-2100000000111100−2i−2i002i2i0000ii00−i−i0
χ21222-12-1222-1-122222-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1002202-1-122-1200000000-1-1-1-12200220000-1-100-1-1000
χ22222-12-1222-1-122222-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1002202-1-122-1200000000-1-1-1-1-2-200-2-20000110011000
χ23222-12-1222-1-122222-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-20-211-2-21-20000000011112i2i00−2i−2i0000−i−i00ii000
χ24222-12-1222-1-122222-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-20-211-2-21-2000000001111−2i−2i002i2i0000ii00−i−i000
χ2522-22-12-122-1-21-2-2-2-21122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100220-222-1-1-2100000000-1-111002-2002-20000-1100-110
χ2622-22-12-122-1-21-2-2-2-21122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100220-222-1-1-2100000000-1-11100-2200-2200001-1001-10
χ2722-22-12-122-1-21-2-2-2-21122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100-2-202-2-2112-10000000011-1-1002i−2i00−2i2i0000−ii00i−i0
χ2822-22-12-122-1-21-2-2-2-21122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100-2-202-2-2112-10000000011-1-100−2i2i002i−2i0000i−i00−ii0
χ2922-2-12-1222-11-2-2-2-2-21122-1-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100220-2-1-1221-200000000-1-1112-2002-20000-1100-11000
χ3022-2-12-1222-11-2-2-2-2-21122-1-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100220-2-1-1221-200000000-1-111-2200-2200001-1001-1000
χ3122-2-12-1222-11-2-2-2-2-21122-1-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100-2-20211-2-2-120000000011-1-12i−2i00−2i2i0000−ii00i−i000
χ3222-2-12-1222-11-2-2-2-2-21122-1-1-122-1-1-1-1-1-122-1-1-1-11111-2-2-2-21111111100-2-20211-2-2-120000000011-1-1−2i2i002i−2i0000i−i00−ii000
χ332-2022-2-222200000000-2-2-222222222-2-2-2-2-2-2-2-200000000000000002i−2i2i−2i002i−2i2i−2i002i2i−2i−2i00002i−2i00000000002-2000000000
χ342-2022-2-222200000000-2-2-222222222-2-2-2-2-2-2-2-200000000000000002i−2i−2i2i00−2i2i−2i2i002i2i−2i−2i0000−2i2i0000000000-22000000000
χ352-2022-2-222200000000-2-2-222222222-2-2-2-2-2-2-2-20000000000000000−2i2i2i−2i002i−2i2i−2i00−2i−2i2i2i00002i−2i0000000000-22000000000
χ362-2022-2-222200000000-2-2-222222222-2-2-2-2-2-2-2-20000000000000000−2i2i−2i2i00−2i2i−2i2i00−2i−2i2i2i0000−2i2i00000000002-2000000000
χ3744444441-244411-2-2441-241-21-211-2-21-21-211-2-211-2-211-2-21111-2-2-2-24400400000001-21-211-2-200000000000000000000000
χ3844444441-244411-2-2441-241-21-211-2-21-21-211-2-211-2-211-2-21111-2-2-2-2-4-400-40000000-12-12-1-12200000000000000000000000
χ394444444-21444-2-21144-214-21-21-2-211-21-21-2-211-2-211-2-211-2-2-2-21111440040000000-21-21-2-21100000000000000000000000
χ404444444-21444-2-21144-214-21-21-2-211-21-21-2-211-2-211-2-211-2-2-2-21111-4-400-400000002-12-122-1-100000000000000000000000
χ41444-2-2-2-2441-2-2444411441-2-2-2-21111-2-2-2-21111-2-2-2-2-2-2-2-211111111004404-2-2-2-2-2-20000000011110000000000000000000
χ42444-2-2-2-2441-2-2444411441-2-2-2-21111-2-2-2-21111-2-2-2-2-2-2-2-21111111100-4-40-422222200000000-1-1-1-10000000000000000000
χ4344-444441-24-4-4-1-122-4-41-241-21-211-2-21-21-211-2-2-1-122-1-122-1-1-1-122224400-400000001-21-2-1-12200000000000000000000000
χ4444-444441-24-4-4-1-122-4-41-241-21-211-2-21-21-211-2-2-1-122-1-122-1-1-1-12222-4-40040000000-12-1211-2-200000000000000000000000
χ4544-44444-214-4-422-1-1-4-4-214-21-21-2-211-21-21-2-21122-1-122-1-12222-1-1-1-14400-40000000-21-2122-1-100000000000000000000000
χ4644-44444-214-4-422-1-1-4-4-214-21-21-2-211-21-21-2-21122-1-122-1-12222-1-1-1-1-4-400400000002-12-1-2-21100000000000000000000000
χ4744-4-2-2-2-244122-4-4-4-4-1-1441-2-2-2-21111-2-2-2-2111122222222-1-1-1-1-1-1-1-100440-4-2-2-2-2220000000011-1-10000000000000000000
χ4844-4-2-2-2-244122-4-4-4-4-1-1441-2-2-2-21111-2-2-2-2111122222222-1-1-1-1-1-1-1-100-4-4042222-2-200000000-1-1110000000000000000000
χ494-4044-4-41-24003-30000-12-41-21-211-2-2-12-12-1-1223-3003-30033-3-300004i−4i0000000000i−2i−i2i3i−3i0000000000000000000000000
χ504-4044-4-41-24003-30000-12-41-21-211-2-2-12-12-1-1223-3003-30033-3-30000−4i4i0000000000−i2ii−2i−3i3i0000000000000000000000000
χ514-4044-4-41-2400-330000-12-41-21-211-2-2-12-12-1-122-3300-3300-3-33300004i−4i0000000000i−2i−i2i−3i3i0000000000000000000000000
χ524-4044-4-41-2400-330000-12-41-21-211-2-2-12-12-1-122-3300-3300-3-3330000−4i4i0000000000−i2ii−2i3i−3i0000000000000000000000000
χ534-4044-4-4-21400003-3002-1-4-21-21-2-2112-12-122-1-1003-3003-3000033-3-34i−4i0000000000−2ii2i−i003i−3i00000000000000000000000
χ544-4044-4-4-21400003-3002-1-4-21-21-2-2112-12-122-1-1003-3003-3000033-3-3−4i4i00000000002i−i−2ii00−3i3i00000000000000000000000
χ554-4044-4-4-2140000-33002-1-4-21-21-2-2112-12-122-1-100-3300-330000-3-3334i−4i0000000000−2ii2i−i00−3i3i00000000000000000000000
χ564-4044-4-4-2140000-33002-1-4-21-21-2-2112-12-122-1-100-3300-330000-3-333−4i4i00000000002i−i−2ii003i−3i00000000000000000000000
χ574-404-2-4244-200000000-4-4244-2-2-2-2-2-2-4-42222220000000000000000004i−4i004i−4i−2i2i0000000000−2i2i000000000000000000000
χ584-404-2-4244-200000000-4-4244-2-2-2-2-2-2-4-4222222000000000000000000−4i4i00−4i4i2i−2i00000000002i−2i000000000000000000000
χ594-40-242-444-200000000-4-42-2-244-2-2-2-222-4-422220000000000000000004i−4i00−2i2i4i−4i0000000000−2i2i000000000000000000000
χ604-40-242-444-200000000-4-42-2-244-2-2-2-222-4-42222000000000000000000−4i4i002i−2i−4i4i00000000002i−2i000000000000000000000
χ614-40-2-2224410000003-3-4-4-1-2-2-2-211112222-1-1-1-1000000003-33-33-33-3004i−4i00−2i2i−2i2i0000000000i−i3i−3i0000000000000000000
χ624-40-2-2224410000003-3-4-4-1-2-2-2-211112222-1-1-1-1000000003-33-33-33-300−4i4i002i−2i2i−2i0000000000−ii−3i3i0000000000000000000
χ634-40-2-222441000000-33-4-4-1-2-2-2-211112222-1-1-1-100000000-33-33-33-33004i−4i00−2i2i−2i2i0000000000i−i−3i3i0000000000000000000
χ644-40-2-222441000000-33-4-4-1-2-2-2-211112222-1-1-1-100000000-33-33-33-3300−4i4i002i−2i2i−2i0000000000−ii3i−3i0000000000000000000
χ658888-48-42-4-48-422-4-4-4-42-4-42-4-12-1-1222-4-12-1-12222-4-4-1-122-1-1-1-122220000000000000000000000000000000000000000000
χ668888-48-4-42-48-4-4-422-4-4-42-4-422-122-1-1-422-122-1-1-4-42222-1-12222-1-1-1-10000000000000000000000000000000000000000000
χ67888-48-482-4-4-4822-4-4-4-42-4-4-122-4-1-122-122-4-1-122-1-12222-4-4-1-1-1-122220000000000000000000000000000000000000000000
χ68888-48-48-42-4-48-4-422-4-4-42-42-1-4222-1-12-1-4222-1-122-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000
χ69888-4-4-4-42-42-4-422-4-4222-42-12-125-4-1-1-12-125-4-1-1-1-122-1-1225-4-45-1-1-1-10000000000000000000000000000000000000000000
χ70888-4-4-4-42-42-4-422-4-4222-42-12-12-45-1-1-12-12-45-1-1-1-122-1-122-455-4-1-1-1-10000000000000000000000000000000000000000000
χ71888-4-4-4-4-422-4-4-4-42222-4222-12-1-1-15-42-12-1-1-15-422-1-122-1-1-1-1-1-15-4-450000000000000000000000000000000000000000000
χ72888-4-4-4-4-422-4-4-4-42222-4222-12-1-1-1-452-12-1-1-1-4522-1-122-1-1-1-1-1-1-455-40000000000000000000000000000000000000000000
χ7388-88-48-42-4-4-84-2-244442-4-42-4-12-1-1222-4-12-1-122-2-24411-2-21111-2-2-2-20000000000000000000000000000000000000000000
χ7488-88-48-4-42-4-8444-2-244-42-4-422-122-1-1-422-122-1-144-2-2-2-211-2-2-2-211110000000000000000000000000000000000000000000
χ7588-8-48-482-4-44-8-2-244442-4-4-122-4-1-122-122-4-1-12211-2-2-2-2441111-2-2-2-20000000000000000000000000000000000000000000
χ7688-8-48-48-42-44-844-2-244-42-42-1-4222-1-12-1-4222-1-1-2-21144-2-2-2-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-4-42-4244-2-244-2-22-42-12-125-4-1-1-12-125-4-1-111-2-211-2-2-544-511110000000000000000000000000000000000000000000
χ7888-8-4-4-4-42-4244-2-244-2-22-42-12-12-45-1-1-12-12-45-1-111-2-211-2-24-5-5411110000000000000000000000000000000000000000000
χ7988-8-4-4-4-4-4224444-2-2-2-2-4222-12-1-1-15-42-12-1-1-15-4-2-211-2-2111111-544-50000000000000000000000000000000000000000000
χ8088-8-4-4-4-4-4224444-2-2-2-2-4222-12-1-1-1-452-12-1-1-1-45-2-211-2-21111114-5-540000000000000000000000000000000000000000000
χ818-808-4-842-4-4006-60000-2442-4-12-1-122-241-211-2-26-600-3300-3-33300000000000000000000000000000000000000000000000
χ828-808-4-842-4-400-660000-2442-4-12-1-122-241-211-2-2-66003-30033-3-300000000000000000000000000000000000000000000000
χ838-808-4-84-42-400006-6004-24-422-122-1-14-2-21-2-211006-600-330000-3-3330000000000000000000000000000000000000000000
χ848-808-4-84-42-40000-66004-24-422-122-1-14-2-21-2-21100-66003-3000033-3-30000000000000000000000000000000000000000000
χ858-80-484-82-4-4006-60000-244-122-4-1-1221-2-2411-2-2-33006-600-3-33300000000000000000000000000000000000000000000000
χ868-80-484-82-4-400-660000-244-122-4-1-1221-2-2411-2-23-300-660033-3-300000000000000000000000000000000000000000000000
χ878-80-484-8-42-400006-6004-242-1-4222-1-1-214-2-2-21100-33006-60000-3-3330000000000000000000000000000000000000000000
χ888-80-484-8-42-40000-66004-242-1-4222-1-1-214-2-2-211003-300-66000033-3-30000000000000000000000000000000000000000000
χ898-80-4-4442-42006-6006-6-24-2-12-125-4-1-11-21-2-5411-3300-3300300-3-33-330000000000000000000000000000000000000000000
χ908-80-4-4442-42006-600-66-24-2-12-12-45-1-11-21-24-511-3300-330003-303-33-30000000000000000000000000000000000000000000
χ918-80-4-4442-4200-66006-6-24-2-12-12-45-1-11-21-24-5113-3003-3000-330-33-330000000000000000000000000000000000000000000
χ928-80-4-4442-4200-6600-66-24-2-12-125-4-1-11-21-2-54113-3003-300-30033-33-30000000000000000000000000000000000000000000
χ938-80-4-444-42200006-66-64-2-22-12-1-1-15-4-21-2111-5400-3300-33-33-33300-30000000000000000000000000000000000000000000
χ948-80-4-444-42200006-6-664-2-22-12-1-1-1-45-21-21114-500-3300-333-33-303-300000000000000000000000000000000000000000000
χ958-80-4-444-4220000-666-64-2-22-12-1-1-1-45-21-21114-5003-3003-3-33-330-3300000000000000000000000000000000000000000000
χ968-80-4-444-4220000-66-664-2-22-12-1-1-15-4-21-2111-54003-3003-33-33-3-30030000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).